The announcement on Thursday listed the name of only one of those hanged, Shukair Farid, a former policeman in the northern city of Mosul.
Farid allegedly confessed that he had worked with Syrian foreign fighters to enlist fellow Iraqis to kill police and civilians.
"The competent authorities have today carried out the death sentences of 13 terrorists," the cabinet announcement said.
Farid had "confessed that foreigners recruited him to spread the fear through killings and abductions", the government said.
A judicial official said the death sentences were handed down in separate trials and were carried out in Baghdad.
"The 13 terrorists were tried in different courts and their trials began in 2005 and ended earlier this year," an official of the Supreme Judiciary Council said, speaking on condition of anonymity because he feared reprisal from insurgents.
Iraq reintroduced the death penalty in June 2004.
"The competent authorities have today carried out the death sentences of 13 terrorists"
Iraqi cabinet announcement
In September 2005, Iraq hanged three convicted murderers, the first executions of convicts since Saddam's overthrow in April 2003. The men, considered common criminals rather than insurgents, were convicted of killing three police officers, kidnapping and rape.
The three men's case took place in court in the Shia city of Kut.
Capital punishment was suspended during the formal US occupation, which ended in June 2004, and the Iraqis reinstated the death penalty two months later for those found guilty of murder, endangering national security and distributing drugs, saying it was necessary to help put down the persistent insurgency.
The authorities also wanted to have the option of executing Saddam if he is convicted of crimes committed by his regime. During Saddam's rule, 114 offences were punishable by death.
Saddam could face the death
penalty if found guilty
Saddam and seven co-defendants are on trial for allegedly massacring more than 140 people in Dujail, north of Baghdad, after an assassination attempt against him there in 1982.
In October, Iraqi lawmakers passed a tough new anti-terrorism law that called for the execution of "those who commit ... terror acts" as well as "those who provoke, plan, finance and all those who enable terrorists to commit these crimes".
Life imprisonment was listed as the punishment for "whoever intentionally conceals terrorist activity or gives shelter to a terrorist for the purpose of hiding him".
Death sentences must be approved by the three-member presidential council headed by President Jalal Talabani, who opposes executions.
In the September hangings and again in the Thursday executions, Talabani refused to sign the authorisation himself but gave his two vice-presidents the authority.